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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 2, Pages 399–417 (Mi izv1689)  

This article is cited in 7 scientific papers (total in 7 papers)

Embedding theorems for profinite groups

V. N. Remeslennikov


Abstract: Suppose that the profinite group $G$ is an extension of $A$ by $H$. In this paper the profinite subgroups of the topological group of continuous maps from $H$ to $A$ are investigated. The results obtained are used to prove topological analogues for profinite groups of the Frobenius and Magnus embedding theorems. Moreover, a sufficient condition is formulated for a pro-$p$-group that is an extension of an abelian group by a finitely presented group to be finitely presented, in the language of complete tensor products of abelian pro-$p$-groups; and this condition is used to prove that a finitely generated metabelian pro-$p$-group is a subgroup of a finitely presented metabelian pro-$p$-group.
Bibliography: 14 titles.

Full text: PDF file (1980 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1980, 14:2, 367–382

Bibliographic databases:

UDC: 519.4
MSC: Primary 20E18, 22A99; Secondary 20F05
Received: 06.01.1978

Citation: V. N. Remeslennikov, “Embedding theorems for profinite groups”, Izv. Akad. Nauk SSSR Ser. Mat., 43:2 (1979), 399–417; Math. USSR-Izv., 14:2 (1980), 367–382

Citation in format AMSBIB
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\by V.~N.~Remeslennikov
\paper Embedding theorems for profinite groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 2
\pages 399--417
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=534600}
\zmath{https://zbmath.org/?q=an:0433.20026|0414.20027}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 2
\pages 367--382
\crossref{https://doi.org/10.1070/IM1980v014n02ABEH001114}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KM96800009}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Jeremy D. King, “Homological finiteness conditions for pro-pgroups”, Communications in Algebra, 27:10 (1999), 4969  crossref
    2. S. G. Melesheva, “Equations and algebraic geometry over profinite groups”, Algebra and Logic, 49:5 (2010), 444–455  mathnet  crossref  mathscinet  zmath  isi  elib
    3. S. G. Afanas'eva, N. S. Romanovskii, “Rigid metabelian pro-$p$-groups”, Algebra and Logic, 53:2 (2014), 102–113  mathnet  crossref  mathscinet  isi
    4. R. Grigorchuk, R. Kravchenko, “On the lattice of subgroups of the lamplighter group”, Int. J. Algebra Comput, 2014, 1  crossref
    5. Ch. K. Gupta, N. S. Romanovskii, “$\mathbb Q$-completions of free solvable groups”, Algebra and Logic, 54:2 (2015), 127–139  mathnet  crossref  crossref  mathscinet  isi
    6. N. S. Romanovskii, “Algebraic sets in a finitely generated rigid $2$-step solvable pro-$p$-group”, Algebra and Logic, 54:6 (2016), 478–488  mathnet  crossref  crossref  mathscinet  isi
    7. S. G. Afanaseva, E. I. Timoshenko, “Partially commutative metabelian pro-$p$-groups”, Siberian Math. J., 60:4 (2019), 559–564  mathnet  crossref  crossref  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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